Mechanical Engineering Principles

Contents

Preface ix

Part 1 Statics and strength of materials 1

1 The effects of forces on materials 1

1.1 Introduction 1

1.2 Tensile force 2

1.3 Compressive force 2

1.4 Shear force 2

1.5 Stress 2

1.6 Strain 3

1.7 Elasticity, limit of

proportionality and elastic limit 6

1.8 Hooke’s law 7

1.9 Ductility, brittleness

and malleability 11

1.10 Modulus of rigidity 12

1.11 Thermal strain 12

1.12 Compound bars 13

2 Tensile testing 18

2.1 The tensile test 18

2.2 Worked problems

on tensile testing 19

2.3 Further worked problems

on tensile testing 21

3 Forces acting at a point 25

3.1 Scalar and vector quantities 25

3.2 Centre of gravity and equilibrium 25

3.3 Forces 26

3.4 The resultant of

two coplanar forces 27

3.5 Triangle of forces method 28

3.6 The parallelogram

of forces method 29

3.7 Resultant of coplanar

forces by calculation 29

3.8 Resultant of more than

two coplanar forces 30

3.9 Coplanar forces in equilibrium 32

3.10 Resolution of forces 34

3.11 Summary 37

4 Forces in structures 40

4.1 Introduction 40

4.2 Worked problems on mechanisms

and pin-jointed trusses 41

4.3 Graphical method 42

4.4 Method of joints (a

mathematical method) 46

4.5 The method of sections

(a mathematical method) 52

Assignment 1 55

5 Simply supported beams 57

5.1 The moment of a force 57

5.2 Equilibrium and the

principle of moments 58

5.3 Simply supported beams

having point loads 61

5.4 Simply supported

beams with couples 64

6 Bending moment and

shear force diagrams

69

6.1 Introduction 69

6.2 Bending moment (M) 69

6.3 Shearing force (F) 69

6.4 Worked problems on

bending moment and

shearing force diagrams 70

6.5 Uniformly distributed loads 78

7 First and second moment of areas 84

7.1 Centroids 84

7.2 The first moment of area 84

7.3 Centroid of area between

a curve and thex-axis 84

7.4 Centroid of area between

a curve and they-axis 85

7.5 Worked problems on

centroids of simple shapes 86

7.6 Further worked problems on

centroids of simple shapes 87

7.7 Second moments of

area of regular sections 88

7.8 Second moment of area

for ‘built-up’ sections 96

Assignment 2 102